That it would be an invitation to embarrassment? That she — at 6 feet 8 inches — would rather dominate in the W.N.B.A. against undersized (or mere) women?

Graciously accommodating, Griner took the high, happy road even if Cuban’s self-promoting spiel was a proposition that could lead only to nowhere good for the cause of gender equity in sports, conceptually speaking.

“When are tryouts?” Griner told reporters Saturday at New Orleans Arena, where the women’s Final Four proceeded Sunday night without her and the tournament favorite, Baylor. “The W.N.B.A. is where I’m at. That is where I’m going. After that, if I get a shot, why turn down something like that? That’s big, even if you don’t make it.”

Actually, it was just the standard big tease, typically propagated by men, and one that — perhaps unintentionally — would make a sideshow out of a player who has been considered revolutionary by women’s basketball standards.

Yes, girls do compete against boys in various sports at the youth and high school levels. Danica Patrick has become a fixture in men’s auto racing. Women like Ann Meyers (now Meyers Drysdale) and Nancy Lieberman took dips in the coed pro basketball pool back when the women’s game was just getting off the developmental launching pad and needed the boost.

But women have worked hard to develop incrementally their own college and professional arenas, their own measures of expectation and excellence. What, exactly, would be the point of setting up the most imposing female player to emerge from the college game to be physically overwhelmed by men?

Why impose male standards on Griner and give those inclined to dwell on such comparisons more ammunition in making the case that the women’s game is inferior?

“His genius would take a huge hit if he drafted Brittney Griner,” Auriemma said. “I think it would be a sham. The fact that a woman could actually play right now in the N.B.A. and compete successfully against the level of play that they have is absolutely ludicrous.”

At least when Auriemma states something so obvious, it is with the credibility of one who has devoted a professional life to fighting pejoratives, stereotypes and pointless apples-versus-oranges comparisons.

When Connecticut approached (and surpassed) U.C.L.A.’s 88-game winning streak, the longest basketball run in N.C.A.A. history, late in 2010, Auriemma fumed or laughed when some critics surmised that the achievement was less worthy.

More recently, he brazenly proposed lowering the rim from 10 feet in the women’s game to adjust for the average player being smaller — in effect saying that women should be confident and independent enough to play by their own rules that work best for them.

Only 22, here to collect more awards for another dominant season on the way to being the likely first pick of the W.N.B.A. draft, by Phoenix, Griner understandably sounded more flattered by the attention than flustered.

“I was like, wow, Mark Cuban, he tweeted me?” Griner said. “It definitely made me feel good, feel special. I tweeted him back, ‘When is tryouts? I can hold my own.’ I’ll try, too. I’m not going to back down from a challenge.”

Serena and Venus Williams dealt with similar pseudo challenges back when they were perceived to be too physically imposing for the women’s tennis tour. Fortunately, that line of thinking died a merciful death. Still dominating the women of her era, Serena can now wage comparative war against the all-timers of her sport.

Why should competing against men — “pushing the envelope,” as Griner called it — be a yardstick for her when the question people should be asking is: how will she fare next summer in the W.N.B.A. against the likes of Tina Charles and Sylvia Fowles? In the women’s game, they have earned that respect and undoubtedly will demand it from Griner when she suits up against them.

“I would hope that she would just stay with the W.N.B.A., because she’s got the opportunity to make a huge impact and continue to prove what we already have,” said Jeff Walz, the Louisville coach, whose physical team defense on Griner was credited in the Round of 16 defeat of Baylor.

And last anyone looked, he didn’t have Dwight Howard or Tyson Chandler defending the paint.

Summing up the story of Griner and Cuban, Walz said: “I’m not sure it would really be for her, or would it be for publicity to try to say, ‘Look what we did in Dallas, look what we’ve done’? ”

Nothing good, in all likelihood, for women’s sports.

A version of this article appears in print on April 8, 2013, on page D3 of the New York edition with the headline: Cuban’s Notion Would Doom Griner To N.B.A. Sideshow. Order Reprints|Today's Paper|Subscribe